# Kaufman's Adaptive Moving Average (KAMA)

Kaufman's Adaptive Moving Average (KAMA) was created by Perry J. Kaufman and presented in 1998 in his book "Trading Systems and Methods, 3rd Edition". The main advantage of KAMA over other moving averages is that it takes into consideration not only the direction, but also the market volatility. KAMA adjusts its length according to the prevailing market conditions.

# Formula

KAMA is calculated by the formula:

$KAMA_{i} = KAMA_{i-1} + sc \times {Price - KAMA_{i-1}}$

where:

$\operatorname{KAMA_{i}}$ is the value of KAMA in the current period.

$\operatorname{KAMA_{i—1}}$ is the value of KAMA in the previous period.

$\operatorname{Price}$ is the price in the current period.

$\operatorname{sc}$ is the smoothing constant calculated each period by the formula:

$sc_{i} = (ER_{i} \times {(fastest - slowest) + slowest})^2$

and

$fastest = \dfrac{2}{\text {Fastest MA Period} + 1}$

$slowest = \dfrac{2}{\text {Slowest MA period} + 1}$

$ER_{i} = \dfrac{|Price_{t} - Price_{t-n}|}{\sum_{i}^{i-n} |Price_{t} - Price_{t-1}|}$

# Usage

The ways of using KAMA are similar to all the moving averages (see Simple Moving Average (MVA, SMA), Exponential Moving Average (EMA)).

Comparing to Simple Moving Average (MVA, SMA), KAMA has less lagging and generates less false signals. Please see indicators on the chart below:

KAMA can also be used to smooth some other technical indicators.